If my supervisor requests formatting that is different from the thesis template, do I need to submit one format to my supervisor and another format to the library?

No.  You can submit the same format to the library. 

While some rules must be followed, others can vary and may be changed (for more details, see Publishing Styles in APA, MLA, Chicago (etc.)).  If you choose to change the formatting in your thesis, this needs to be done by modifying the appropriate styles.  Changing the formatting manually (one-by-one) may adversely affect the output in the PDF.  You can learn how to modify your styles in the Thesis Template: Fine-tuning & Trouble-shooting Workshop.